# Since the function plot_city_figures is dependent on other variables and functions defined earlier,
# we need to ensure they are all available in the current scope.
# We already have eigenValues and eigenVectors sorted, so we will create a StandardScaler object again.
# StandardScaler object for later inverse transform
from sklearn.preprocessing import StandardScaler
original_df = data_raw
scaler = StandardScaler().fit(original_df)
X_std = scaler.transform(original_df)
# Compute sorted eigenvalues and eigenvectors
# This uses the previously computed covariance matrix 'C'
eigenValues, eigenVectors = np.linalg.eigh(C)
args = (-eigenValues).argsort()
sorted_eigenvalues = eigenValues[args]
sorted_eigenvectors = eigenVectors[:, args]
def plot_city_figures(original_df, city_names):
# Plot the original time-series for the specified city
fig, axes = plt.subplots(len(city_names), 1, figsize=(20, len(city_names) * 5), sharex=True)
if len(city_names) == 1:
axes = [axes] # Ensure axes is a list even for one city
for i, city in enumerate(city_names):
city_data = original_df.loc[city].values
axes[i].plot(original_df.columns, city_data)
axes[i].set_title(f"Temperature Time Series for {city}")
axes[i].set_xlabel('Date')
axes[i].set_ylabel('Temperature')
selected_dates = original_df.columns[::12]
axes[i].set_xticks(selected_dates)
plt.show()
# The incremental reconstruction of the original time-series for city
for city in city_names:
city_data_std = X_std[original_df.index == city]
PC_count = [1, 2, 4, 8, 16]
plt.figure(figsize=(20, 7))
plt.plot(original_df.columns, original_df.loc[city].values, label='Original Data', color='black', linewidth=2)
for pc in PC_count:
W = sorted_eigenvectors[:, :pc]
projX = np.dot(city_data_std, W)
# Reconstruction
ReconX = scaler.inverse_transform(np.dot(projX, W.T))
plt.plot(original_df.columns, ReconX.flatten(), label=f'Reconstruction with {pc} PCs')
plt.title(f"Incremental Reconstruction of {city}'s Time-Series")
plt.xlabel('Date')
plt.ylabel('Temperature')
selected_dates = original_df.columns[::12]
plt.xticks(selected_dates)
plt.legend()
plt.show()
# Calculate best reconstruction residual error and generate a plot
for city in city_names:
city_data_std = X_std[original_df.index == city]
# Best reconstruction is when there are 16 principal components
W = sorted_eigenvectors[:, :16]
projX = np.dot(city_data_std, W)
best_recon = scaler.inverse_transform(np.dot(projX, W.T))
residuals = original_df.loc[city].values - best_recon.flatten()
plt.figure(figsize=(15, 7))
plt.plot(residuals, label='Residual Error', color='red')
plt.title(f"Residual Error for {city}'s Time-Series Reconstruction")
plt.xlabel('Date')
plt.ylabel('Residual Error')
plt.legend()
plt.show()
RMSE_values_PCA = []
for city in city_names:
city_data_std = X_std[original_df.index == city]
RMSE_values = []
for pc in range(1, 11):
W = sorted_eigenvectors[:, :pc]
projX = np.dot(city_data_std, W)
ReconX = scaler.inverse_transform(np.dot(projX, W.T))
RMSE = np.sqrt(np.mean((original_df.loc[city].values - ReconX.flatten()) ** 2))
RMSE_values.append(RMSE)
plt.figure(figsize=(15, 7))
plt.plot(range(1, 11), RMSE_values, 'o-')
plt.title(f"RMSE of the Reconstruction for {city}")
plt.xlabel('Number of Components')
plt.ylabel('RMSE')
plt.xticks(range(1, 11))
plt.grid(True)
plt.show()
RMSE_values_PCA.append(RMSE_values)
return RMSE_values_PCA
city_names = ['Yakeshi','Zamboanga','Norilsk', 'Juliaca', 'Doha']
RMSE_values_PCA = plot_city_figures(original_df, city_names)
